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The cutting power of preparation

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Author Info
Tercieux, Olivier (Dept. of Econometrics and OR, Tilburg University, The Netherlands)
Voorneveld, Mark () (Dept. of Economics, Stockholm School of Economics)

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Abstract

In a strategic game, a curb set [Basu and Weibull, Econ. Letters 36 (1991) 141] is a product set of pure strategies containing all best responses ro every possible belief restricted to this set. Prep sets [Voorneveld, Games Econ. Behav. 48 (2004) 403] relax this condition by only requiring the presence of at least one best response to such a belief. The purpose of this paper is to provide economically interesting classes of games in which minimal prep sets give sharp predictions, whereas in relevant subclasses of these games, minimal curb sets have no cutting power whatsoever and simply consist of the entire strategy space. These classes include potential games, congestion games with player-specific payoffs, and supermodular games.

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Publisher Info
Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 583.

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Length: 23 pages
Date of creation: 31 Jan 2005
Date of revision:
Handle: RePEc:hhs:hastef:0583

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Related research
Keywords: curb sets; prep sets; potential games; congestion games; supermodular games;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September. [Downloadable!] (restricted)
  2. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Blackwell Publishing, vol. 42(1), pages 45-61, March. [Downloadable!] (restricted)
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  3. Voorneveld, M. & Borm, P. & Megen, F. van, 1999. "Congestion games and potentials reconsidered," Discussion Paper 98, Tilburg University, Center for Economic Research. [Downloadable!]
  4. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November. [Downloadable!] (restricted)
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  5. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June. [Downloadable!] (restricted)
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  6. Kets, Willemien & Voorneveld, Mark, 2005. "Learning to be prepared," Discussion Paper 117, Tilburg University, Center for Economic Research. [Downloadable!]
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  7. Voorneveld, Mark & Kets, Willemien & Norde, Henk, 2005. "An axiomatization of minimal curb sets," Working Paper Series in Economics and Finance 589, Stockholm School of Economics, revised 18 Mar 2005. [Downloadable!]
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  8. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March. [Downloadable!] (restricted)
  9. Thomas Quint & Martin Shubik, 1994. "A Model of Migration," Cowles Foundation Discussion Papers 1088, Cowles Foundation, Yale University. [Downloadable!]
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  11. Kosfeld, Michael & Droste, Edward & Voorneveld, Mark, 2002. "A myopic adjustment process leading to best-reply matching," Games and Economic Behavior, Elsevier, vol. 40(2), pages 270-298, August. [Downloadable!] (restricted)
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  12. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November. [Downloadable!] (restricted)
  13. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January. [Downloadable!] (restricted)
  14. Slikker, Marco, 2001. "Coalition Formation and Potential Games," Games and Economic Behavior, Elsevier, vol. 37(2), pages 436-448, November. [Downloadable!] (restricted)
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  15. Voorneveld, Mark, 1997. "Equilibria and approximate equilibria in infinite potential games," Economics Letters, Elsevier, vol. 56(2), pages 163-169, October. [Downloadable!] (restricted)
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  16. Hurkens, Sjaak, 1996. "Multi-sided Pre-play Communication by Burning Money," Journal of Economic Theory, Elsevier, vol. 69(1), pages 186-197, April. [Downloadable!] (restricted)
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  17. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  18. Vitaly Pruzhansky, 2003. "On finding curb sets in extensive games," International Journal of Game Theory, Springer, vol. 32(2), pages 205-210, December. [Downloadable!] (restricted)
  19. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March. [Downloadable!] (restricted)
  20. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. [Downloadable!] (restricted)
  21. Voorneveld, Mark, 2005. "Persistent retracts and preparation," Games and Economic Behavior, Elsevier, vol. 51(1), pages 228-232, April. [Downloadable!] (restricted)
  22. Vitaly Pruzhansky, 2003. "On Finding Curb Sets in Extensive Games," Tinbergen Institute Discussion Papers 03-098/1, Tinbergen Institute. [Downloadable!]
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  25. Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Kets, W. & Voorneveld, M., 2007. "Congestion, Equilibrium and Learning: The Minority Game," Discussion Paper 2007-61, Tilburg University, Center for Economic Research. [Downloadable!]
  2. Kets, W., 2007. "The Minority Game: An Economics Perspective," Discussion Paper 2007-53, Tilburg University, Center for Economic Research. [Downloadable!]
  3. Kets, Willemien & Voorneveld, Mark, 2005. "Learning to be prepared," Discussion Paper 117, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  4. Willemien Kets, 2007. "The minority game: An economics perspective," Quantitative Finance Papers 0706.4432, arXiv.org. [Downloadable!]
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